Pseudo-differential operators in several p-adic variables and sub-Markovian semigroups

This article marks the inaugural exploration of certain classes of negative or positive definite functions in several p-adic variables. Associated with these functions, two classes of pseudo-differential operators, convolution semigroups, some positive measures and \(L^{2}(\mathbb {Q}_{p}^{n})\) $L^2({\mathbb{Q}}_p^n)$ -sub-Markovian semigroups are introduced.